One of my problems with the modeling of searches by William Dembski and Robert Marks is that I don't see how every assisted search can be described as a probability measure on the space of the feasible searches. But nevertheless, Winston Ewert insisted that

All assisted search, irrespective of the manner in which they are assisted, can be modeled as a probably distribution biased towards selecting elements in the target.

Marks and Dembski claim that the average active information is a measure of search performance - at least they write in their remark:

If no information about a search exists, so that the underlying measure is uniform, then, on average, any other assumed measure will result in negative active information, thereby rendering the search performance worse than random search.

Their erratum seems indeed to proof the remark in a slightly modified way:

Given a uniform distribution over targets of cardinality k, and baseline uniform distribution, the average active information will be non-positive

(The proof of this statement in the erratum is correct - at least as far as I can see...)
So, lets play a game: From a deck of cards one is chosen at random. If you want to play, you have to pay 1\$, and you get 10\$ if you are able to guess the card correctly. But you are not alone, there are three other people A, B and (surprisingly) C who'll announce their guesses first. They use the following search strategies:

A: he will announce a card according to the uniform distribution

B: he will always announce ♦2

C: He has access to a very powerful oracle, which gives him the right card. Unfortunately - due to an old superstition - he is unable to say ♦2, so every time this card appears he will announce another one at random

Which strategy will you follow? Siding with player A or B gives you a chance of 1/52 for a correct guess, so you will loose on average ca. 81¢ per game. However, if you pose your bet with C, you will win 8.81$ a game in the long run! That's because the probability of a correct guess is 1/52 for both our players A and B, while C's chance for success is 51/52.

But what would Marks, Dembski or Ewert do? They calculate the average active information according to the formula given in the erratum. This E[I+] is 0 for player A, but -∞ for B and C. As negative active information on average renders the search performance worse than random search, they have to stick with player A.

So, either average active information is not a good measure of search performance, or not every assisted search, irrespective of the manner in which they are assisted can be modeled as a probably distribution. Or it is a bit of both...

You also make brief mention that the HNFLT proof assumes a partition of the search space and thus cannot handle the overlapping targets. This is problematic because any target on the original search space will become an overlapping target on the multi-query search space. I think you are correct on this point. Thanks for bringing it to our attention. We've added a description of the problem as well as an alternate proof for the uniform case on overlapping targets to the pdf: http://evoinfo.org/papers/2010_TheSearchForASearch.pdf.

Tuesday, May 15, 2012

The post before this one was UD’s 9,000th. Thank you to all of our readers for your support as we celebrate this milestone.

So congratulations! But a comment by SCheesman pours a little water into the celebratory wine:

I wish I could celebrate, but I fear 9000 is a reflection of a vast inflation in the number rate of postings in the last year or two, with a corresponding decline in comments.
I owe a good deal of what I know today about ID from UD, both from a scientific and theological perspective, and used to enjoy the long threads and back-and-forth between proponents and opponents.
But now, many, if not most posts get nary a comment, and the ones engendering some debate often are lost in the crowd. Since the recent purge of participants who failed to pass what amounted to a purity test, it’s been pretty quiet here. The most lively recent discussion featured a debate between OEC’s and YEC’s. Now I enjoy that sort of thing (like on Sal Cordova’s old “Young Cosmos” blog), but it’s hardly what UD used to be known for.
Maybe the new format gets more visitors than it used to, but I’d be interested in seeing the stats, including comments per post, posts per month, unique visitors etc. over the last few years.
I miss the old days. I expect a lot of us do.